Related papers: Word maps with small image in simple groups
We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$, distinct from the identity, such that $w$ contains $m(f)$. We show that every infinite word contains an imaged factor of length at…
Let $G$ be a $(2,m,n)$-group and let $x$ be the number of distinct primes dividing $\chi$, the Euler characteristic of $G$. We prove, first, that, apart from a finite number of known exceptions, a non-abelian simple composition factor $T$…
A graph $G=(V,E)$ is a \emph{word-representable graph} if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. In this paper we give an effective…
Different classes of communication network topologies and their representation in the form of adjacency matrix and its eigenvalues are presented. A self-organizing feature map neural network is used to map different classes of communication…
Word complexity is defined in a number of different ways. Psycholinguistic, morphological and lexical proxies are often used. Human ratings are also used. The problem here is that these proxies do not measure complexity directly, and human…
We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some…
Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of…
We provide geometric methods and algorithms to verify, construct and enumerate pairs of words (of specified length over a fixed $m$-letter alphabet) that form identities in the semigroup $\ut{n}$ of $n\times n$ upper triangular tropical…
Waring's classical problem deals with expressing every natural number as a sum of g(k) k-th powers. Recently there has been considerable interest in similar questions for nonabelian groups, and simple groups in particular. Here the k-th…
Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…
Considering that words with different characteristic in the text have different importance for classification, grouping them together separately can strengthen the semantic expression of each part. Thus we propose a new text representation…
Given any generating set of any pseudo-Anosov-containing subgroup of the mapping class group of a surface, we construct a pseudo-Anosov with word length bounded by a constant depending only on the surface. More generally, in any subgroup G…
Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in…
We present enumerations of a class of maps on Klein bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein bottle. These are of…
The article describes a model of automatic analysis of puns, where a word is intentionally used in two meanings at the same time (the target word). We employ Roget's Thesaurus to discover two groups of words which, in a pun, form around two…
We introduce language-driven image generation, the task of generating an image visualizing the semantic contents of a word embedding, e.g., given the word embedding of grasshopper, we generate a natural image of a grasshopper. We implement…
This paper demonstrates a task to finetune a BART model so it can construct a sentence from an arbitrary set of words, which used to be a difficult NLP task. The training task is making sentences with four words, but the trained model can…
We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.
A graph $G=(V,E)$ is word-representable if and only if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $xy\in E$. A split graph is a graph in which the vertices can be…
We investigate the least number of palindromic factors in an infinite word. We first consider general alphabets, and give answers to this problem for periodic and non-periodic words, closed or not under reversal of factors. We then…